Description of the internal format of the line number table

Conceptually, the line number table consists of a sequence of triples:
    start-offset (inclusive), end-offset (exclusive), line-number.

Note that not all byte codes have a line number so we need handle `None` for the line-number.

However, storing the above sequence directly would be very inefficient as we would need 12 bytes per entry.

First, note that the end of one entry is the same as the start of the next, so we can overlap entries.
Second, we don't really need arbitrary access to the sequence, so we can store deltas.

We just need to store (end - start, line delta) pairs. The start offset of the first entry is always zero.

Third, most deltas are small, so we can use a single byte for each value, as long we allow several entries for the same line.

Consider the following table
     Start    End     Line
      0       6       1
      6       50      2
      50      350     7
      350     360     No line number
      360     376     8
      376     380     208

Stripping the redundant ends gives:

   End-Start  Line-delta
      6         +1
      44        +1
      300       +5
      10        No line number
      16        +1
      4         +200


Note that the end - start value is always positive.

Finally, in order to fit into a single byte we need to convert start deltas to the range 0 <= delta <= 254,
and line deltas to the range -127  <= delta <= 127.
A line delta of -128 is used to indicate no line number.
Also note that a delta of zero indicates that there are no bytecodes in the given range,
which means we can use an invalid line number for that range.

Final form:

   Start delta   Line delta
    6               +1
    44              +1
    254             +5
    46              0
    10              -128 (No line number, treated as a delta of zero)
    16              +1
    0               +127 (line 135, but the range is empty as no bytecodes are at line 135)
    4               +73

Iterating over the table.
-------------------------

For the `co_lines` method we want to emit the full form, omitting the (350, 360, No line number) and empty entries.

The code is as follows:

def co_lines(code):
    line = code.co_firstlineno
    end = 0
    table_iter = iter(code.internal_line_table):
    for sdelta, ldelta in table_iter:
        if ldelta == 0: # No change to line number, just accumulate changes to end
            end += sdelta
            continue
        start = end
        end = start + sdelta
        if ldelta == -128: # No valid line number -- skip entry
            continue
        line += ldelta
        if end == start: # Empty range, omit.
            continue
        yield start, end, line




The historical co_lnotab format
-------------------------------

prior to 3.10 code objects stored a field named co_lnotab.
This was an array of unsigned bytes disguised as a Python bytes object.

The old co_lnotab did not account for the presence of bytecodes without a line number,
nor was it well suited to tracing as a number of workarounds were required.

The old format can still be accessed via `code.co_lnotab`, which is lazily computed from the new format.

Below is the description of the old co_lnotab format:


The array is conceptually a compressed list of
    (bytecode offset increment, line number increment)
pairs.  The details are important and delicate, best illustrated by example:

    byte code offset    source code line number
        0                   1
        6                   2
       50                   7
      350                 207
      361                 208

Instead of storing these numbers literally, we compress the list by storing only
the difference from one row to the next.  Conceptually, the stored list might
look like:

    0, 1,  6, 1,  44, 5,  300, 200,  11, 1

The above doesn't really work, but it's a start. An unsigned byte (byte code
offset) can't hold negative values, or values larger than 255, a signed byte
(line number) can't hold values larger than 127 or less than -128, and the
above example contains two such values.  (Note that before 3.6, line number
was also encoded by an unsigned byte.)  So we make two tweaks:

 (a) there's a deep assumption that byte code offsets increase monotonically,
 and
 (b) if byte code offset jumps by more than 255 from one row to the next, or if
 source code line number jumps by more than 127 or less than -128 from one row
 to the next, more than one pair is written to the table. In case #b,
 there's no way to know from looking at the table later how many were written.
 That's the delicate part.  A user of co_lnotab desiring to find the source
 line number corresponding to a bytecode address A should do something like
 this:

    lineno = addr = 0
    for addr_incr, line_incr in co_lnotab:
        addr += addr_incr
        if addr > A:
            return lineno
        if line_incr >= 0x80:
            line_incr -= 0x100
        lineno += line_incr

(In C, this is implemented by PyCode_Addr2Line().)  In order for this to work,
when the addr field increments by more than 255, the line # increment in each
pair generated must be 0 until the remaining addr increment is < 256.  So, in
the example above, assemble_lnotab in compile.c should not (as was actually done
until 2.2) expand 300, 200 to
    255, 255, 45, 45,
but to
    255, 0, 45, 127, 0, 73.

The above is sufficient to reconstruct line numbers for tracebacks, but not for
line tracing.  Tracing is handled by PyCode_CheckLineNumber() in codeobject.c
and maybe_call_line_trace() in ceval.c.

*** Tracing ***

To a first approximation, we want to call the tracing function when the line
number of the current instruction changes.  Re-computing the current line for
every instruction is a little slow, though, so each time we compute the line
number we save the bytecode indices where it's valid:

     *instr_lb <= frame->f_lasti < *instr_ub

is true so long as execution does not change lines.  That is, *instr_lb holds
the first bytecode index of the current line, and *instr_ub holds the first
bytecode index of the next line.  As long as the above expression is true,
maybe_call_line_trace() does not need to call PyCode_CheckLineNumber().  Note
that the same line may appear multiple times in the lnotab, either because the
bytecode jumped more than 255 indices between line number changes or because
the compiler inserted the same line twice.  Even in that case, *instr_ub holds
the first index of the next line.

However, we don't *always* want to call the line trace function when the above
test fails.

Consider this code:

1: def f(a):
2:    while a:
3:       print(1)
4:       break
5:    else:
6:       print(2)

which compiles to this:

  2           0 SETUP_LOOP              26 (to 28)
        >>    2 LOAD_FAST                0 (a)
              4 POP_JUMP_IF_FALSE       18

  3           6 LOAD_GLOBAL              0 (print)
              8 LOAD_CONST               1 (1)
             10 CALL_NO_KW               1
             12 POP_TOP

  4          14 BREAK_LOOP
             16 JUMP_ABSOLUTE            2
        >>   18 POP_BLOCK

  6          20 LOAD_GLOBAL              0 (print)
             22 LOAD_CONST               2 (2)
             24 CALL_NO_KW               1
             26 POP_TOP
        >>   28 LOAD_CONST               0 (None)
             30 RETURN_VALUE

If 'a' is false, execution will jump to the POP_BLOCK instruction at offset 18
and the co_lnotab will claim that execution has moved to line 4, which is wrong.
In this case, we could instead associate the POP_BLOCK with line 5, but that
would break jumps around loops without else clauses.

We fix this by only calling the line trace function for a forward jump if the
co_lnotab indicates we have jumped to the *start* of a line, i.e. if the current
instruction offset matches the offset given for the start of a line by the
co_lnotab.  For backward jumps, however, we always call the line trace function,
which lets a debugger stop on every evaluation of a loop guard (which usually
won't be the first opcode in a line).

Why do we set f_lineno when tracing, and only just before calling the trace
function?  Well, consider the code above when 'a' is true.  If stepping through
this with 'n' in pdb, you would stop at line 1 with a "call" type event, then
line events on lines 2, 3, and 4, then a "return" type event -- but because the
code for the return actually falls in the range of the "line 6" opcodes, you
would be shown line 6 during this event.  This is a change from the behaviour in
2.2 and before, and I've found it confusing in practice.  By setting and using
f_lineno when tracing, one can report a line number different from that
suggested by f_lasti on this one occasion where it's desirable.
